Strain, stress and energy in lipid bilayer induced by electrostatic/electrokinetic forces

Lipid bilayer was deformed by the electrostatic/electrokinetic forces induced by the fixed charges on the top monolayer-solution interface. The strains, stresses and energy were simulated using finite element method. The elastic moduli of the heads were four times greater than those of tails sections, but were individually isotropic. The physics of the situation was evaluated using a coupled system of linear elastic equations and electrostatic-electrokinetic (Poisson-Nernst-Planck) equations. The Coulomb force (due to fixed charges in the electric field), and the dielectric force (due to uneven electric field and the solution-membrane permittivity mismatch) bend the membrane, but unevenly. Whereas the bottom monolayer extends vertically (towards charged surface), the top monolayer compresses. In contrast the top monolayer extends horizontally, but the bottom monolayer compresses. The horizontal normal stress is higher in the heads than in the tails sections, but is similar in two monolayers, whereas the vertical normal stress is small. The horizontal normal stress is associated with horizontal normal strain, and vertical with both vertical and horizontal strain. Surprisingly, the shear stress (an indicator where the membrane will deform), is greater in the tails sections. Finally, the elastic energy (which is clearly greater in the heads sections) is dominated by its horizontal component and peaks in the middle of the membrane. The shear component dominates in the tails sections, and is minimal in the membrane center. Even spatially uniform external force thus leads to complex membrane deformation and generates complex profiles of stress and elastic energy.